Can someone please help me with this one

Step-by-step explanation:

The transformations we typically study are ...

  g(x) = -f(x) . . . vertical reflection

  g(x) = f(x) +h . . . vertical shift up by h

  g(x) = k·f(x) . . . vertical expansion by a factor of k

  g(x) = f(-x) . . . horizontal reflection

  g(x) = f(x -h) . . . right shift by h

  g(x) = f(k·x) . . . horizontal compression by a factor of k

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You have g(x)=3f(-(x-2)) +1.

The external factor of 3 is a vertical stretch.

The minus sign multiplying the argument of f(x) is a horizontal reflection.*

The -2 in parentheses is a right shift of 2.

The +1 added to the function value is a shift up by 1.

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* The parent function is symmetrical about the y-axis, so a horizontal reflection does not change the graph in any way. It may as well be ignored. However, the sign shows up in the transformation, so we have listed it--even though you cannot detect it in the graph.

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In the attached, f(x) is shown as a blue dashed line.

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8